Redo the fish tank problem seen in class, but now include the nitrogen gas as well into the system, along with the previously existing components. Use all the data from before. Assume that the Henry’s Law constant for nitrogen in water (Hn,w) at 25°C is 87008.55 atm and for oxygen in water (Ho,w) at the same temperature = 42538.46 atm. Does your pet fish still have enough dissolved oxygen in the tank to survive? (Minimum mole fraction of dissolved oxygen required by a typical fish is around 4 x 10-6 ). Hints: a. Assume that there are 2 moles of O2 for every 8 moles of N2 in air (this will serve as your 4th equation) to solve for the 4 unknowns (xo, xn, yo, yn). b. Use steam tables to find Psat for water, instead of using Antoine equation. P=1atm P_{w}^{sat}=0.0313
P = 1 atm
Pwsat = 0.0313 atm
Net total pressure of air = 1 - 0.0313 = 0.9687 atm
According to Daltons Law:
PO2 + PN2 = P
P. yo + P. yn = P
yo + yn = 1
Also given that : yn = 4 yo
Therefore, we have
yo = 0.2
yn = 0.8
PO2 = 0.2 X P = 0.2 X 0.9687 = 0.19374 atm
PN2 = 0.8 X P = 0.8 X 0.9687 = 0.77496 atm
Using henry's law;
xo = PO2 / Ho = 0.19374/42538.46 = 4.55 X 10-6
xn = Pn2 / Hn = 0.77496/87008.55 = 8.91 X 10-6
For fish to survive, xo > 4 X 10-6
Here xo = 4.55 X 10-6
Hence the fish will survive.
Redo the fish tank problem seen in class, but now include the nitrogen gas as well...